If the dose is still considered as a quantitative covariate, then the Tukey trend test [1]} can be used, namely simultaneous considering three regression models for the metameters \(D_i\) , \(rank(D_i)\)  and \(log(D_i)\) , [2]}, providing the joint distribution for this maximum test by means of multiple marginal models (mmm) [3]}. This requires the formulation of logistic regression models, but allows extensions in generalized linear (mixed) models - a second issue discussed here. Exactly where modifications of the original CA-test are difficult, e.g. the adjustments against covariates, two-way to hierarchical designs, overdispersed proportions instead of simple table data, multi-center studies, repeated measurements, multiple endpoints, among others.
